Use vector method to find the area of the triangle with vertices A, B, C that shown in the figure below: A(3,1,4) B(-3,5,1) -> yk C(0,5,-4)

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

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Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

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Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: find a vector that is orthogonal to (1,2,3) and (4,5,6). do not use cross product.

A: Let's find vector that is orthogonal to given two vectors.

Q: The cross product of vectors a = (-1, 4, 6) and b = (3, 0, -2) is %3D

A: The cross product of vectors is given below

Q: Do the vectors ū = i+j-4k, V= -5i +3j-7k and w'= -i +4j+2k plane? 1ie in the Same

A: We have to check whether the vectors u→=i+2j-4k, v→=-5i+3j-7k, and w→=-i+4j+2k are in the same…

Q: Find the B-coordinate vector for p(t) = -6+10t-7t² B={1-2t+t², 4-7t +5t², 5-8t+8t²} Enter your…

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Q: det pC-1,2,-1) and Q(2,-7,8) be two points in three dimenonal space. Use vectors to fird the points…

A: Vector form of a point: Let (a, b, c) are any point in 3D- space. Then this point can be expressed…

Q: Vector A is 6 inches long and is 60° above the +x-axis in the first quadrant. While vector B is 6…

A: Shown here are two vectors as given in the question. Resolve the first and second vector on the x…

Q: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then,…

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Q: Q3/A/ If ā = i – 2j + k , Find: i) (ā x b). (ā x c) ii) (ā × 5) × (ā x c) tho vectors 2i - i+ 2k and…

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Q: (d) comp5 (e) projzā

A: Here we want to find component of vector b along the vector a . And  Projection of vector a along…

Q: In R^3, consider the three points A(2, -1, 4), B(3, 4, -2) and C(-1, 2, 7). (a) By an appropriate…

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